Add to ORKGAbstract. Given a linear operator A which satisfies a generalized dissipativity condition in terms of a “uniqueness function ” w and its nonlinear continuous perturbation B in a real Banach space X, we discuss the construction of a nonlinear semigroup S providing mild solutions for the semilinear abstract Cauchy problem (SP) u ′ = (A + B)u(t), t> 0 and u(0) = x. It is shown that a subtangential condition and a semilinear stability condition are altogether necessary and sufficient for the generation of the semigroup S. A concrete example to which these generation results are applicable is also provided
The paper is devoted to the problem of existence of propagators for an abstract linear non-autonomou...
The aim of this paper is to show an application of the recently introduced B-bounded semigroups in t...
summary:The aim of this paper is to give an existence theorem for a semilinear equation of evolution...
Abstract. Let X be a real Banach space, let A: D(A) ⊂ X → X be the generator of a (C0)-contraction ...
This book presents a systematic exposition of the general theory of nonlinear contraction semigroups...
This paper is concerned with the existence and stability of solutions of a class of semilinear nonau...
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipa...
AbstractIn this paper we study existence, uniqueness, and stability of nonlinear evolution equations...
Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolut...
Abstract An approximation theory for semilinear evolution equations is treated in terms of convergen...
Abstract. Given a semilinear problem of the form (SP) u′(t) = (A+B)u(t), t> 0; u(0) = x ∈ D ⊂ X...
In this paper we consider the questions of existence and uniqueness of solutions of certain semiline...
A class of nonlinear evolution operators is introduced and a characterization of continuous in nites...
We prove the existence of regular solutions for the quasi-linear evolution $$ {d over dt}(x(t)+g(t,x...
AbstractLet E be a Banach space such that both E and its dual space are uniformly convex. In this pa...
The paper is devoted to the problem of existence of propagators for an abstract linear non-autonomou...
The aim of this paper is to show an application of the recently introduced B-bounded semigroups in t...
summary:The aim of this paper is to give an existence theorem for a semilinear equation of evolution...
Abstract. Let X be a real Banach space, let A: D(A) ⊂ X → X be the generator of a (C0)-contraction ...
This book presents a systematic exposition of the general theory of nonlinear contraction semigroups...
This paper is concerned with the existence and stability of solutions of a class of semilinear nonau...
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipa...
AbstractIn this paper we study existence, uniqueness, and stability of nonlinear evolution equations...
Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolut...
Abstract An approximation theory for semilinear evolution equations is treated in terms of convergen...
Abstract. Given a semilinear problem of the form (SP) u′(t) = (A+B)u(t), t> 0; u(0) = x ∈ D ⊂ X...
In this paper we consider the questions of existence and uniqueness of solutions of certain semiline...
A class of nonlinear evolution operators is introduced and a characterization of continuous in nites...
We prove the existence of regular solutions for the quasi-linear evolution $$ {d over dt}(x(t)+g(t,x...
AbstractLet E be a Banach space such that both E and its dual space are uniformly convex. In this pa...
The paper is devoted to the problem of existence of propagators for an abstract linear non-autonomou...
The aim of this paper is to show an application of the recently introduced B-bounded semigroups in t...
summary:The aim of this paper is to give an existence theorem for a semilinear equation of evolution...